Now showing items 41-60 of 82

    • On Particle Interaction Models 

      Banerjee, Sayan (2014-02-24)
      This dissertation deals with three problems in Stochastic Analysis which broadly involve interactions, either between particles (Chapters 1 and 2), or between particles and the boundary of a C2 domain (Chapter 3). In Chapter ...
    • On special Lagrangian equations 

      Wang, Dake (2014-02-24)
      In this paper we study the special Lagrangian equation and related equations. Special Lagrangian equation originates in the special Lagrangian geometry by Harvey-Lawson [HL1]. In subcritical phases, we construct singular ...
    • Lam-Williams Markov chains on symmetric groups 

      Huynh, Anh Trung (2014-02-24)
      This paper reviews the current state of the Lam-Williams conjectures on a multivariate Markov chain on the symmetric group S_n. We start with Lam's work on random core partitions which led to a remarkable Markov chain on ...
    • Combinatorial Laguerre Series 

      Taylor, Jair Patrick (2014-02-24)
      We develop a method for counting words subject to various restrictions by finding a combinatorial interpretation for a product of weighted sums of Laguerre polynomials. We describe how such a series can be computed by ...
    • The Positive Semidefinite Rank of Matrices and Polytopes 

      Robinson, Richard
      The positive semidefinite (psd) rank of a nonnegative <italic>p</italic> × <italic>q</italic> matrix <italic>M</italic> is defined to be the smallest integer <italic>k</italic> such that there exist <italic>k</italic> × ...
    • Interacting particle systems with partial annihilation through membranes 

      Fan, Wai Tong
      This thesis studies the <italic>hydrodynamic limit</italic> and the <italic>fluctuation limit</italic> for a class of interacting particle systems in domains. These systems are introduced to model the transport of positive ...
    • Self-shrinking Solutions to Mean Curvature Flow 

      Drugan, Gregory
      We construct new examples of self-shrinking solutions to mean curvature flow. We first construct an immersed and non-embedded sphere self-shrinker. This result verifies numerical evidence dating back to the 1980's and shows ...
    • Brownian Motion on Spaces with Varying Dimension 

      Lou, Shuwen
      In this thesis we introduce and study Brownian motion with or without drift on state spaces with varying dimension. Starting with a concrete such state space that is the plane with an infinite pole on it, we construct a ...
    • Dual Equivalence Graphs and their Applications 

      Roberts, Austin
      In 2007 Sami Assaf introduced dual equivalence graphs as a method for demonstrating that a quasisymmetric function is Schur positive. The method involves the creation of a graph whose vertices are weighted by Ira Gessel's ...
    • Time-like graphical models 

      Tadic, Tvrtko
      We study continuous processes indexed by a special family of graphs. Processes indexed by vertices of graphs are known as probabilistic graphical models. In 2011, Burdzy and Pal proposed a continuous version of graphical ...
    • Arithmetic Properties of the Derived Category for Calabi-Yau Varieties 

      Ward, Matthew J
      This thesis develops a theory of arithmetic Fourier-Mukai transforms in order to obtain results about equivalences between the derived category of Calabi-Yau varieties over non-algebraically closed fields. We obtain answers ...
    • Shimura Degrees for Elliptic Curves over Number Fields 

      Deines, Alyson Laurene
      A crowning achievement of Number theory in the 20th century is a theorem of Wiles which states that for an elliptic curve E over <bold>Q</bold> of conductor N, there is a non-constant map from the modular curve of level N ...
    • Three Problems in Discrete Probability 

      Slivken, Erik Dustin
      In this thesis we present three problems. The first problem is to find a good description of the number of fixed points of a 231-avoiding permutation. We use a bijection from Dyck paths to 231-avoiding permutations that ...
    • The regularity of Loewner curves 

      Tran, Huy Vo
      The Loewner differential equation, a classical tool that has attracted recent attention due to Schramm-Loewner evolution (SLE), provides a unique way of encoding a simple 2-dimensional curve into a continuous 1-dimensional ...
    • Inverse Boundary-Value Problems on an Infinite Slab 

      Marinov, Kaloyan
      In this work, we study the stability aspect of two inverse boundary-value problems (IBVPs) on an infinite slab with partial data. The uniqueness aspects of these IBVPs were considered and studied by Li and Uhlmann for the ...
    • Eigenvalue fluctuations for random regular graphs 

      Johnson, Tobias Lee
      One of the major themes of random matrix theory is that many asymptotic properties of traditionally studied distributions of random matrices are <italic>universal</italic>. We probe the edges of universality by studying ...
    • The Grothendieck Groups of Module Categories over Coherent Algebras 

      Sisodia, Gautam
      Let <italic>k</italic> be a field and <italic>B</italic> either a finitely generated free <italic>k</italic>-algebra, or a regular <italic>k</italic>-algebra of global dimension two with at least three generators, generated ...
    • Classification of connected Hopf algebras up to prime-cube dimension 

      Wang, Xingting
      We classify all connected Hopf algebras up to p^3 dimension over an algebraically closed field of characteristic p>0 under the mild restriction such that in dimension p^3, we only work over odd primes p when the primitive ...
    • Local Set Approximation: Infinitesimal to Local Theorems for Sets in Euclidean Space and Applications 

      Lewis, Stephen
      In this thesis we develop the theory of Local Set Approximation (LSA), a framework which arises naturally from the study of sets with singularities. That is, we describe the local structure of a set A in Euclidean space ...
    • Conformal welding of uniform random trees 

      Barnes, Joel
      A conformally balanced tree is an embedding of a given planar map into the plane with constraints on the harmonic measure of its edges such that the resulting set is unique up to scale and rotation. Bishop (2013) showed ...